Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
134 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C4⋊#226 | C7 | direct (N × H) |
| 56. C4×C7 | #226 | semidirect |
| 85. C7 | C4⋊#226 | direct (N × H) |
| 94. C4 | C7×#226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#226 | 2 |
| C4×C7×SL(2,𝔽3) | 2 |
| C7×#462 | 3 |
| C7×C4⋊Dic3 | 4 |
| C4⋊#226 | 7 |